Materials not showing in object mode or render view
Your eye is made of two spheres, one with the iris and pupil textures and a second that surrounds the first which I expect you plan to put a transparent texture that also adds the part in front of the iris.

This second sphere has no texture yet, which is why it hides the inner sphere when rendering. Also you have hidden the vertices for this outer sphere in edit mode which allows you to see the inner sphere in edit mode.

Press &#9095; AltH while in edit mode to unhide the vertices, you can then select the outer sphere and assign a transparent texture to finish your eye.